Construction of quasi-periodic solutions for delayed perturbation differential equations

TL;DR

This paper develops a novel approach using multi-scale analysis to construct quasi-periodic solutions for delayed differential equations, expanding the application of KAM and space splitting techniques.

Contribution

It introduces a new application of multi-scale analysis to non-selfadjoint delayed differential equations, complementing existing KAM and space splitting methods.

Findings

Successfully constructs quasi-periodic solutions for DDEs.

Demonstrates the effectiveness of multi-scale analysis in non-selfadjoint problems.

Provides a new example of applying advanced analytical techniques to delayed perturbation equations.

Abstract

We employ the Craig-Wayne-Bourgain method to construct quasi-periodic solutions for delayed perturbation differential equations. Our results not only implement the existing literatures on constructing quasi-periodic solutions for DDE by the KAM method and space splitting technique, but also provide an example of application of multi-scale analysis method to non-selfadjoint problem.